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Combinations or Permutations

Practice deciding which to use
by

Loryl Bedinger

on 17 December 2013

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Transcript of Combinations or Permutations

1.
Amy chooses 3
books from 7 on
the shelf.
Is this a combination or a permutation?
3.
There are 10 cyclists in a race. The first 3 finishers win prize money. First place wins $500, Second place wins $300, and Third place wins $100.
Is this a combination or permutation?
Process
Ask yourself:

Does the order matter?
This is a combination. The order in
which the students choose the questions,
does not matter. They will still be answering
the same questions.

Now, solve using the formula for combinations:
Choose 5 questions from a group of 8 questions.
2.
On a test, students
must choose 5 questions
from a group of 8
questions.
Combinations or Permutations?
an arrangement of items in which order DOES NOT matter!
Ex. Choosing Pizza Toppings: If sausage, pepperoni and mushrooms are
on a pizza, it is no different from a pizza that has mushrooms, sausage
and pepperoni. Same toppings!! Order DOES NOT matter.
an arrangement of items in which order DOES matter.
Ex. How runners finish a race. 1st- Kory, 2nd- Ally, 3rd- Drey. or 1st- Ally, 2nd- Kory, 3rd- Drey. They are different because ORDER matters.
This is a combination, because the order does not matter.

Now, solve! Use the formula for combinations to find how many combinations of 3 books Amy can take from 7.
35
Is this a combination
or permutation?
56
This is a permutation! The order in which the runners finish the race DOES matter.

Now, solve using the formula for permutations:
10 runners and only the top 3 finishers win prize money.
720
4.
Seven students are standing in line in the school cafeteria. In how many different orders can they be standing in line?
This is a Permutation. The order in which they stand in line DOES MATTER! Especially if they run out of lunches before the end of the line. =)

Now, solve using the formula for permutations. If there are 7 students, how many different ways can they stand in line?
5040
5.
How many different 5-player teams
could you make with 15 players?
This is a Combination! It is a combination because order DOES NOT matter.

Now, solve using the formula for combinations.
How many different 5-player teams can you make with 15 players?
3003
Full transcript